Rethinking Prediction Horizons: Decoupling Model Queries from State Updates in Few-Step MeanFlow

Tinglan Wang; Haixu Liu; Shaobo Chen; Nuo Qian; Qi Gao; Kai Wen; Yu Yao

cs.LGOct 14, 2026

Rethinking Prediction Horizons: Decoupling Model Queries from State Updates in Few-Step MeanFlow

Authors: Tinglan Wang, Haixu Liu, Shaobo Chen, Nuo Qian, Qi Gao, Kai Wen, Yu Yao

Organizations: Beijing QBoson Quantum Technology Co., Ltd. · University of Sydney

Abstract

MeanFlow predicts interval-average velocities, but conventional few-step sampling ties the interval queried from the model to the duration of the state update. We separate these two quantities at inference, fixing the model, update grid, and number of queries while varying the prediction horizon. Our central finding is that the horizon response depends on both query position and the states entering that query. Across seven independently trained CIFAR-10 checkpoints at classifier-free guidance (CFG) scale 2, a longer horizon worsens FID at early steps but improves it at the midpoint. To probe whether query time alone determines this response, we fix the midpoint query and current/subsequent guidance while changing only earlier CFG. In held-out factorial outcomes on five previously studied checkpoints, the mean midpoint horizon benefit increases from 0.109 to 1.308 FID, indicating sensitivity to the incoming-state distribution. A frozen four-query rule reduces mean CIFAR-10 FID by 2.023 without retraining or extra queries, including gains on five checkpoints trained after rule selection. A milder rule also improves mean FID by 1.041 on a stronger frozen grid, with fixed-rule FID gains on the evaluated public ImageNet-256 and AFHQ checkpoints. However, matched-budget calibration favors query-start shifting in historical CIFAR tests, and the tested Horizon allocation adds no FID benefit beyond Grid+Start on two public ImageNet models. Thus, prediction horizon is a distinct, position- and state-sensitive inference control, but not a universally preferred one.

Figures & tables

Figure 1: Horizon response reverses with position and changes with earlier guidance. Left: seven CIFAR checkpoints at CFG 2, with pointwise 95% Student-

t

intervals across checkpoints. Right: five checkpoints with held-out factorial outcomes compare midpoint

h_{2}=.50

versus

.25

after prefix CFG 1 or 1.5; current/later CFG stays 1.5. Lines connect the same checkpoint. Both panels use paired 10k samples per cell, but different guidance settings and checkpoint subsets.

Figure 2: The prediction horizon can exceed the update duration. Curved arrows show prediction intervals; gray arrows show physical updates. Only the midpoint horizon changes from

.25

.50

. Both samplers use four updates of duration

.25

and four velocity queries (eight backbone forwards with two-pass CFG).

State grid	Checkpoints	FID gain [95% interval]	FID/KID wins
Uniform	Prospective five	1.906 $[1.772,2.040]$	5/5; 5/5
Uniform	All seven	2.023 $[1.820,2.226]$	7/7; 7/7
Frozen stronger grid	Same five	1.015 $[0.922,1.108]$	5/5; 5/5
Frozen stronger grid	All seven	1.041 $[0.960,1.122]$	7/7; 7/7

Table 1: Horizon gains persist on a stronger frozen state grid. FID gains (Local minus Horizon) and FID/KID wins at CFG 2, four queries, and 50k generated / 50k real images. Means weight checkpoints equally; brackets are descriptive 95% Student-

t

intervals across checkpoints. At the changed query,

h/\delta

is 2 on the uniform grid and 1.2 on the stronger grid. Protocols: Appendix B .

Figure 3: The original two-checkpoint CFG-2 comparison illustrates comparable Local/Horizon inference costs, not a broad Pareto frontier. (a) FID values match Table 6 B; query counts appear in parentheses. (b) The five methods with measured median latency use Table 9 (batch 128); the selected grid has no measured timing point. Lower FID is better. Calibrated Start/Horizon at CFG 1.5 are a separate protocol (Table 2 ).

A: Calibrated rules, CFG 1.5; 50k generated / 50k real
Rule	FID $\downarrow$	KID $\times 10^{3}\downarrow$	DINO $\downarrow$	DINO P	DINO R
Local	10.272	5.782	–	–	–
Calibrated Horizon	8.878	4.831	–	–	–
Calibrated Start	8.311	3.538	–	–	–
B: Identical saved pixels, CFG 1.5; 10k generated / 10k real
Local	14.212	5.811	150.730	0.7171	0.3617

Table 2: Start leads on FID/KID, while Horizon yields lower DINO distance. Means over seven reused checkpoints; four queries, CFG 1.5. Generated/real counts are 50k/50k in A and separate 10k/10k sets in B; compare within panels. B uses identical image bytes across evaluators. P/R denote DINO precision/recall; dashes denote unmeasured metrics. Details: Appendices C.1 and D .

Model	Grid+Start	Grid+Start+Horizon	Restored $h=\delta$
B/2	7.2227	7.2498	7.2743
XL/2	4.7969	4.8327	4.8327

Table 3: The tested Horizon allocation adds no FID benefit. Mean FID (

\downarrow

) over two paired 10k confirmations, using four queries and external CFG 1 with learned guidance retained. GS and GSH have equal new budgets but nonnested candidate sets. The last column restores

h=\delta

in the selected GSH setting, keeping its grid and query starts fixed. Protocol: Appendix C.5 .

Seed	NFE	Local	Fixed H	Cal. H	Cal. Start	Mixed (choice)
700081	2	15.122	n/a	15.122	15.122	15.122 (Local)
700081	4	14.123	13.670	12.632	12.844	12.632 (H)
700081	8	13.061	13.009	12.771	12.680	12.680 (Start)
700087	2	15.075	n/a	15.075	15.075	15.075 (Local)
700087	4	14.326	13.848	12.648	12.912	12.648 (H)
700087	8	13.288	13.234	12.997	12.989	12.989 (Start)

Table 4: On new training seeds, the FID-selected control changes with NFE. Mean FID (

\downarrow

) over two paired 10k confirmations at CFG 1.5, against 10k real images. Fixed H uses midpoint

h/\delta=1.2

; this extension is infeasible at NFE 2 (n/a). Cal. H/Start select within the named family plus Local; Mixed includes both families, with its choice in parentheses. Candidate sets, budgets and other metrics: Appendix F .

Appendix figures & tables28 assets

Supplementary material from the paper’s appendix.

Appendix

\delta_{k}\leftarrow t_{k+1}-t_{k},\qquad v_{k}\leftarrow u_{\theta}(x_{k},\tau_{k},h_{k}),\qquad x_{k+1}\leftarrow x_{k}+\delta_{k}v_{k}.

Appendix

Algorithm 1: A fixed state grid with independently specified query intervals. Local MeanFlow is recovered by

\tau_{k}=t_{k}

and

h_{k}=\delta_{k}

Cohort	Checkpoints	Role and replication unit
Original CIFAR	300007, 300017	Two training units; three paired 50k repeats each
Prospective extension	700001, 700027, 700057, 700067, 700079	Five new training units; one paired 50k repeat each
Later blind study	700081, 700087	Two separate new units; NFE 2/4/8, two 10k confirmations per selected setting
Historical CIFAR transfer	Seeds 42, 123, 2027 in each of three pairing recipes	Reused historical models; separate transfer evidence
Public ImageNet	MeanFlow-B/2, MeanFlow-XL/2, AlphaFlow-B/2	Three public checkpoints, not common-architecture seed replication
AFHQv2	Two corrected and two QMAC-trained checkpoints	Four held-out checkpoints in two training families

Appendix

Table 5: Evidence cohorts are kept separate. Additional metrics or generation repeats do not increase the number of independently trained models.

State grid	Checkpoints	Local FID	Horizon FID	Gain [95% interval]	FID/KID wins
Uniform	Prospective five	12.168	10.262	1.906 $[1.772,2.040]$	5/5; 5/5
Uniform	All seven	12.241	10.218	2.023 $[1.820,2.226]$	7/7; 7/7
Best of 84	Same five	11.197	10.182	1.015 $[0.922,1.108]$	5/5; 5/5
Best of 84	All seven	11.236	10.195	1.041 $[0.960,1.122]$	7/7; 7/7

Appendix

Table 6: Primary efficacy and fixed-grid control at CFG 2. A separates the prospective subgroup from the combined cohort. Intervals are descriptive 95% Student-

t

intervals across checkpoints. B is the original two-checkpoint head-to-head comparison, with three paired 50k repeats per checkpoint. “Best of 84” denotes a finite-grid winner, not a family optimum.

Train seed	Uniform repeats	Cohort	Uniform-grid gain		Frozen-grid gain
			FID	KID $\times 10^{3}$	FID	KID $\times 10^{3}$
300007	3	original	2.3628	1.755	1.1835	.794
300017	3	original	2.2657	1.629	1.0269	.674
700001	1	prospective	1.8780	1.374	.9956	.665
700027	1	prospective	1.7943	1.317	.9203	.574
700057	1	prospective	1.8535	1.354	.9859	.657

Appendix

Table 7: Paired Local-minus-Horizon effects on the same seven training checkpoints. Uniform and frozen-grid protocols are separate comparisons. Frozen-grid effects use one 50k repeat per checkpoint. Per-arm absolute scores and every generation-repeat row remain in the archived full tables; their rounded differences are not used to recompute aggregates.

State time	Queried horizons	Mean FID gains	Positive checkpoints
0	.25,.375,.50,.625,.75,.875,1	.000,-.798,-2.220,-3.855,-5.639,-7.531,-9.732	0/7,0/7,0/7,0/7,0/7,0/7,0/7
.25	.25,.375,.50,.625,.75	.000,-.031,-.092,-.280,-.837	0/7,2/7,1/7,1/7,0/7
.50	.25,.30,.35,.40,.45,.50	.000,+.489,+.970,+1.414,+1.774,+2.010	0/7,7/7,7/7,7/7,7/7,7/7

Appendix

Table 8: Full position-scan means. Positive gain favors the intervention. The local

h=.25

entries are exact zero contrasts, not failed replications.

Sampler	Velocity queries	CIFAR ms (batch 128)	ImageNet ms (batch 16)
Local	4	342.09	212.71
Horizon	4	344.93	212.54
Local	5	431.59	226.56
Continuous lookahead	5	435.29	225.35
Local	6	519.91	238.95

Appendix

Table 9: Interleaved median inference latency, copied from the frozen timing audit. Horizon changes the four-query median by +.83% on CIFAR and -.08% on ImageNet. Query counts are velocity evaluations; CFG call accounting is specified by the corresponding model protocol.

Panel of Figure 4 — Figure 4: Paired, non-curated previews. CIFAR uses checkpoint 300007 and generation seed 20261001 (64 images per arm); ImageNet uses public MeanFlow-B/2 and seed 20261061 (16 images per arm); AFHQ uses corrected MeanFlow seed 2027 and generation seed 20261072 (64 images per arm). All use four uniform updates and Local $h=.25$ ; the Horizon midpoint is $.50$ for CIFAR, $.30$ for ImageNet and the calibrated $.325$ for AFHQ. These are different dataset-specific comparisons. Display images use JPEG compression; their source identities are retained in the figure manifest. Similarity at page scale does not imply identical distributions.

Rule	$\tau_{2}$	$h_{2}$	FID	KID $\times 10^{3}$	P	R
Local	.500	.250000	14.204	5.811	.746	.419
State grid	.800	.100000	12.908	4.764	.744	.438
Start	.575	.250000	12.380	3.506	.672	.506
Horizon	.500	.489583	12.902	4.901	.649	.545
Joint	.400	.500000	12.216	3.335	.737	.465

Appendix

Table 10: CIFAR 25-candidate winners and original 10k confirmation means over seven reused checkpoints. P/R use VGG16 features. Other queries are local; state-grid search instead uses

T=(0,.4,.8,.9,1)

. All families have equal additional development counts.

Rule	Dataset	Units	FID wins	FID gain	KID gain
Tuned	CIFAR-10	7	7/7	2.023	0.001456
Tuned	AFHQv2-256	4	4/4	0.212	mixed
$\rho=1.2$	CIFAR, three recipes	9	9/9	0.490	0.000397
$\rho=1.2$	ImageNet-256	3	3/3	0.111	–
$\rho=1.2$	AFHQv2-256	4	4/4	0.194	.000098

Appendix

Table 11: Earlier cross-dataset evidence. Gains are Local minus Horizon. “Units” denotes independent training seeds for tuned CIFAR and evaluated checkpoints otherwise; public ImageNet models are not repeated training seeds of one architecture.

Checkpoint	Repeats	Local FID	Horizon FID	Gain	Relative
MeanFlow-B/2	1	5.1859	5.0551	.1308	2.52%
MeanFlow-XL/2	3	2.6300	2.5326	.0974	3.70%
AlphaFlow-B/2	3	5.0633	4.9570	.1063	2.10%

Appendix

Table 12: Original fixed-rule ImageNet transfer: four uniform updates, third-query

h=.30

versus

.25

, 50k samples per repeat. Repeats share each public checkpoint’s weights. Relative gain divides paired mean FID gain by mean Local FID.

Checkpoint	Local	Horizon	Inherited Start
MeanFlow-B/2	5.13619 / 245.217	5.00426 / 242.393	5.63790 / 211.474
MeanFlow-XL/2	2.61386 / 288.267	2.51254 / 286.031	2.87045 / 255.497
AlphaFlow-B/2	4.95572 / 243.945	4.84760 / 241.635	5.55436 / 212.154

Appendix

Table 13: Later fixed-rule 50k confirmation. Each entry is FID / IS. These samples are separate from Table 12 ; none of the three rules is calibrated on these target outputs.

Grid / external CFG	Model	Start $\tau$	Horizon $h$	Local	Start	Horizon
Narrow / 1	B/2	.5250	.325	7.4992 / 190.41	7.2680 / 187.38	7.3439 / 187.21
Narrow / 1	XL/2	.5500	.325	5.0265 / 222.08	4.8885 / 211.31	4.9159 / 219.12
Narrow / .8	B/2	.5000	.250	7.5811 / 147.15	7.5811 / 147.15	7.5811 / 147.15
Narrow / .8	XL/2	.5000	.225	4.9491 / 175.21	4.9491 / 175.21	4.9421 / 176.38
Range / 1	B/2	.5375	.400	7.4987 / 191.03	7.2297 / 184.14	7.3075 / 183.24
Range / 1	XL/2	.5375	.400	5.0728 / 219.59	4.8566 / 214.59	4.9277 / 213.02

Appendix

Table 14: Target-calibration confirmation means over two new 10k repeats. Each score is FID / IS; queries are the frozen winners. Local is always

(.50,.25)

. CFG strata and later ranges remain separate. All repeat-level values and SDs are archived.

Model	Local	Start	Horizon	Joint
B/2	7.5071 / 188.03	7.2339 / 182.83	7.3282 / 180.92	8.0472 / 166.11
XL/2	5.0275 / 219.95	4.8304 / 214.39	4.8879 / 212.36	5.4654 / 197.56

Appendix

Table 15: Fixed composition: two-repeat 10k means, reported as FID / IS. Joint changes both coordinates to

(.5375,.40)

. All four arms use external CFG 1 and four backbone calls.

Model	Repeat	GS FID	GSH FID	Restored FID	$A$	$B$	Min. IS ratio
B/2	1	7.2216	7.2564	7.2808	-0.0347	+0.0244	0.9941
B/2	2	7.2238	7.2433	7.2678	-0.0195	+0.0245	0.9956
XL/2	1	4.8049	4.8307	4.8307	-0.0258	+0.0000	1.0000
XL/2	2	4.7888	4.8347	4.8347	-0.0459	+0.0000	0.9949

Appendix

Table 16: Both fresh 10k confirmation repeats.

A=\mathrm{FID}(\mathrm{GS})-\mathrm{FID}(\mathrm{GSH})

compares selected allocations;

B=\mathrm{FID}(\mathrm{restored})-\mathrm{FID}(\mathrm{GSH})

isolates horizon at the selected grid/start. Positive favors GSH. The last column is the smaller of the GSH/GS and GSH/restored IS ratios. Repeats use seeds 2026092692 and 2026092693; they are sampling repeats on fixed public weights.

Contrast	$\Delta$ FID	95% interval	Lower	$\Delta$ KID	95% interval	Lower
Horizon – Local	-1.298	$[-1.472,-1.123]$	7/7	-0.898	$[-1.064,-0.732]$	7/7
Start – Local	-1.824	$[-2.130,-1.517]$	7/7	-2.296	$[-2.714,-1.879]$	7/7
Horizon – Start	+0.526	$[+0.206,+0.846]$	0/7	+1.398	$[+0.900,+1.896]$	0/7

Appendix

Table 17: Inception contrasts after reevaluation on the saved DINO input bytes. Changes are first arm minus second; negative values favor the first arm. Intervals are descriptive 95% Student-

t

intervals across checkpoints. Both KID columns are scaled by

10^{3}

Contrast	$\Delta$ distance	95% interval	Lower	$\Delta$ P (pp)	$\Delta$ R (pp)
Horizon – Local	-3.132	$[-4.104,-2.160]$	7/7	-2.04	+3.05
Start – Local	+14.690	$[+11.789,+17.591]$	0/7	-3.50	+0.33
Horizon – Start	-17.822	$[-19.846,-15.798]$	7/7	+1.46	+2.72

Appendix

Table 18: DINO contrasts on the same 21 saved image cells. Changes are first arm minus second. Distance decreases are preferable; P/R changes are percentage points (pp). The distance intervals describe variation over the seven reused checkpoints. P/R are separate coordinates.

Arm	Old FID	New FID	$\Delta$ FID	95% interval	Old KID	New KID	$\Delta$ KID
Local	14.204	14.212	+.0074	$[+.0025,+.0124]$	5.8109	5.8106	-.0003
Start	12.380	12.388	+.0078	$[+.0022,+.0134]$	3.5057	3.5144	+.0087
Horizon	12.902	12.914	+.0121	$[+.0076,+.0166]$	4.9006	4.9125	+.0119

Appendix

Table 19: Rounded-input reevaluation versus original truncation-input Inception measurements. Changes are new minus original. KID columns are scaled by

10^{3}

. All checkpoint cells and KID sensitivity intervals remain in the archive.

Cohort	Train seed	$G_{1}$	$G_{1.5}$	$D=G_{1.5}-G_{1}$	$D_{\rm KID}\times 10^{3}$
Pilot	300007	0.1992	1.5668	1.3676	1.3368
Pilot	300017	0.4131	1.6243	1.2112	1.1190
Replication	700001	0.1046	1.2689	1.1642	1.1723
Replication	700027	0.1701	1.2305	1.0604	1.1565
Replication	700057	-0.1728	1.1677	1.3405	1.3043
Replication	700067	0.0941	1.2851	1.1910	1.1661

Appendix

Table 20: Guidance-prefix contrasts.

G_{p}

is local-minus-horizon FID after prefix CFG

p

, with both suffix steps fixed at CFG

1.5

. Pilot repeats are averaged within checkpoint. The replication hypothesis and settings were frozen after the two-checkpoint pilot and before the five new factorial evaluations.

	FID $\downarrow$		KID $\times 10^{3}\downarrow$
Checkpoint	Local	Horizon	Local	Horizon
Local MAC s42 (dev.)	16.7540	16.7410	10.5848	10.9653
Paired recipe s300007	15.9024	16.0348	9.4296	9.9692
Paired recipe s300017	15.7868	15.6920	9.3806	9.6567

Appendix

Table 21: Existing full-trajectory CFG-1 results: one paired 10k generation repeat per checkpoint against a fixed class-balanced 10k real subset. All weights were trained locally; the MAC baseline is not a released checkpoint. Seed 42 was development; the paired-recipe seeds reuse historical weights. Inception uses the historical float-input normalize=True path, not the rounded-uint8 same-pixel protocol of Appendix D . The historical sampler still executes eight backbone calls.

Panel	Existing training seeds	Repeats/model	Images
Projection	300007, 300017	2	160,000
Equal norm	700001, 700027	1	100,000
Signed dose	700057, 700067	1	100,000
Prefix	700057, 700067	1	120,000

Appendix

Table 22: Directional panels: 48 unique 10k cells, ten checkpoint–generation jobs, six existing weights and no new training. Every arm is retained in the portable numeric ledger.

Panel	Treatment / reference	FID gain	DINO gain
Projection	Residual / Local	+2.817	+16.560
	Full / Projected	+0.850	+10.077
	Projected / Local	+0.745	-5.899
Equal norm	Residual / scaled Full	+1.165	+9.728
	Residual / Random	+2.352	+14.456
Signed	$+r$ / $-r$	+7.158	+78.923

Appendix

Table 23: Selected contrasts retain the adverse controls. Gains are reference minus treatment; positive favors the treatment. These checkpoint means summarize the sequential panels, not an equal-cost sampler comparison. Tables 24 and 25 give all gate minima and signed doses; the complete 48 cells and precision/recall remain in the unchanged evidence ledger and archive.

Panel	Contrast / gate	Units	Min. FID	Min. DINO	FID margin
Projection	Full / Local (prereq.)	4 pairs	+1.5006	+2.7743	–
	Residual / Local	4 pairs	+2.6896	+15.0465	+2.6608
	Full / Projected	4 pairs	+0.6452	+8.9053	+0.5967
Equal norm	Residual / Local	2 models	+2.3228	+15.4099	+2.2728
	Residual / scaled Full	2 models	+0.9694	+9.1436	+0.9194
	Residual / Random	2 models	+2.2298	+14.4043	+2.1798

Appendix

Table 24: Weakest observed unit for every frozen directional gate. Gains are reference minus treatment; prefix interactions are high-prefix minus low-prefix gains. Min. FID/DINO range over the stated units, which may attain their minima on different units. The final column is the minimum checkpoint-mean FID gain minus the frozen

.05

threshold. Projection has two repeats per model, whereas all other panels have one repeat per model. The prerequisite requires positivity only. All shown minima and margins pass; these are descriptive gates, not significance tests.

	Checkpoint 700057			Checkpoint 700067
Dose $\alpha$	FID	KID $\times 10^{3}$	DINO	FID	KID $\times 10^{3}$	DINO
$-1$	19.3259	8.0277	214.1753	19.6556	7.9593	221.1238
$-0.5$	16.4837	6.9552	176.1563	16.5493	6.7097	180.4755
0 (Local)	14.6940	6.2627	153.9113	14.5998	5.9022	156.5978
$+0.5$	13.4437	5.5216	142.4353	13.2309	5.0992	144.1813
$+1$	12.4814	4.6672	138.1119	12.1843	4.2334	139.3422

Appendix

Table 25: All five frozen signed doses on both existing models. Each checkpoint–dose combination uses one 10k sample set at generation seed 202619261 with the stated midpoint velocity

v_{0}+\alpha r

; all other settings match the signed panel. Lower is better for all three distances. Their decline across the five doses is observed on each model; monotonicity was not a selection rule or frozen success criterion.

Seed	NFE	Fixed H	Cal. H	Cal. Start	Mixed
700081	2	Local ∗	Local	Local	Local
700081	4	$h_{2}$	$h_{4}$	$s_{4}$	$h_{4}$
700081	8	$h_{2}$	$h_{4}$	$s_{4}$	$s_{4}$
700087	2	Local ∗	Local	Local	Local
700087	4	$h_{2}$	$h_{4}$	$s_{4}$	$h_{4}$
700087	8	$h_{2}$	$h_{4}$	$s_{4}$	$s_{4}$

Appendix

Table 26: All selected roles; Local is always the shared reference. ∗ Fixed extension is infeasible at NFE 2. At NFE 4 Mixed equals calibrated Horizon; at NFE 8 it equals calibrated Start. These identities explain the repeated values in the main table without counting duplicate generations.

Seed	NFE	Arm	FID $\downarrow$	KID $\times 10^{3}\downarrow$	DINO $\downarrow$	Prec. $\uparrow$	Rec. $\uparrow$
700081	2	Local	15.1220	6.2885	167.175	0.7097	0.3176
700081	4	Local	14.1230	5.6144	145.831	0.7145	0.3684
700081	4	$h_{2}$	13.6702	5.2822	142.588	0.7109	0.3803
700081	4	$h_{4}$	12.6322	4.5026	139.306	0.6953	0.4072
700081	4	$s_{4}$	12.8443	3.9415	158.941	0.6902	0.3768
700081	8	Local	13.0614	4.7497	137.521	0.7184	0.3905

Appendix

Table 27: Every unique selected intervention, averaging its two paired 10k repeats. There are 18 unique model–NFE–candidate combinations and 36 confirmation cells. The original 30 role means are recoverable using Table 26 . Precision and recall use DINOv2 features; all KID estimator SDs and F-scores remain in the unchanged numeric ledger. Rows are deduplicated by candidate identity, not by similar scores.

Seed	NFE	Treatment / reference	$\Delta$ FID r1	$\Delta$ FID r2	KID gain $\times 10^{3}$	DINO gain	Gate
700081	4	Fixed H / Local	+0.4531	+0.4526	+0.3322	+3.244	Pass
700081	4	Cal. H / Local	+1.5073	+1.4743	+1.1117	+6.526	Pass
700081	4	Cal. H / Start	+0.1650	+0.2591	-0.5612	+19.636	Pass
700081	8	Fixed H / Local	+0.0512	+0.0544	+0.0459	+0.223	Pass
700081	8	Cal. H / Start	-0.1095	-0.0738	-0.3317	+4.507	Fail
700087	4	Fixed H / Local	+0.4771	+0.4779	+0.3441	+2.733	Pass

Appendix

Table 28: Key paired contrasts retain both FID repeat gains and mean KID/DINO gains (reference minus treatment; positive is favorable). Gates test FID/DINO only. All 34 registered contrasts, including exact-zero identities and all precision/recall flags, remain in the ledger. NFE 2 contrasts are zero because every calibrated strategy selects Local.

		Agreement with 5k choice			Confirmation FID difference
NFE	Seed	500	1k	2k	1k	2k
4	700081	19/20	20/20	20/20	+0.00000	+0.00000
4	700087	20/20	20/20	20/20	+0.00000	+0.00000
8	700081	6/20	10/20	14/20	+0.04582	+0.02749
8	700087	4/20	6/20	9/20	+0.00539	+0.00423

Appendix

Table 29: Post-hoc sample-budget sensitivity of the frozen five-candidate Mixed strategy. Budgets are samples per candidate (nominal strategy totals: 2.5k, 5k and 10k). Agreement counts reuse 20 subsets of one stored pool. FID differences compare the selected candidate with the original 5k choice on the existing two confirmation repeats, and are then averaged across subset selections; positive is worse. Both 1k/2k columns have complete confirmation coverage. They are not oracle regret or 20 independent confirmations.

$t_{k}$	$h_{k}$	FID gain r1	FID gain r2	Mean FID gain	IS retention
0.00	0.30	-0.1171	-0.0992	-0.1081	0.9817
0.00	0.50	-2.8806	-2.9079	-2.8942	0.8698
0.25	0.30	-0.0518	-0.0280	-0.0399	0.9947
0.25	0.50	-2.2329	-2.1834	-2.2082	0.8608
0.50	0.30	+0.0016	+0.0064	+0.0040	0.9790
0.50	0.50	-1.1703	-1.1361	-1.1532	0.8744

Appendix

Table 30: Native iMF-XL/2 fixed position–horizon panel. Two new generation repeats, each 10k, at native guidance 4. FID gains are paired Local minus intervention; positive is better. IS retention is the mean ratio to that local arm. This is one checkpoint; the largest panel gain is an exploratory maximum.

Few-Step Diffusion Sampling

Few-step diffusion sampling develops ways to generate data with far fewer denoising evaluations while retaining quality and diversity.

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Apr 10, 2026

Discrete Meanflow Training Curriculum

Flow-based image generative models exhibit stable training and produce high quality samples when using multi-step sampling procedures. One-step generative models can produce high quality image samples but can be difficult to optimize as they often exhibit unstable training dynamics. Meanflow models exhibit excellent few-step sampling performance and tantalizing one-step sampling performance. Notably, MeanFlow models that achieve this have required extremely large training budgets. We significantly decrease the amount of computation and data budget it takes to train Meanflow models by noting and exploiting a particular discretization of the Meanflow objective that yields a consistency property which we formulate into a ``Discrete Meanflow'' (DMF) Training Curriculum. Initialized with a pretrained Flow Model, DMF curriculum reaches one-step FID 3.36 on CIFAR-10 in only 2000 epochs. We anticipate that faster training curriculums of Meanflow models, specifically those fine-tuned from existing Flow Models, drives efficient training methods of future one-step examples.

Chia-Hong Hsu, Frank Wood

Department of Computer Science, University of British Columbia, Vancouver, BC, Canada

Flow-Based Generative Modeling MeanFlow One-Step Generative Modeling

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Aug 5, 2026

Rethinking Pixel Mean Flows via Interval Denoiser

Modern diffusion and flow-based models are increasingly moving toward few-step, latent-free generation to bypass the computational overhead of multi-step sampling and the reconstruction bottlenecks of external autoencoders. We propose the Interval Denoiser, a theoretically rigorous framework for latent-free generation. Derived directly from the flow matching ODE, it establishes an exact analytical mapping for intermediate trajectory states. Unlike prior formulations, our prediction is shown to reside on a low-dimensional manifold across any time interval, making the regression tractable for a network operating directly on pixels. Furthermore, by avoiding empirical algebraic substitutions, our formulation correctly isolates the pure time derivative to prevent biased gradient evaluations and ensure exact first-order optimization. By analyzing this objective, we equip our framework with residual clipping and a time-sampling curriculum, enabling effective long-interval training and improving few-step performance. Trained from scratch on ImageNet 256x256, our model achieves an FID of 4.55 in one step (1-NFE) and 3.98 in two steps (2-NFE) without perceptual losses.

Alexander Zaytsev, Dmitry Baranchuk, Alexander Korotin +1

HSE University · Yandex Research · Applied AI Institute +2

Flow Matching Image Generation One-Step Generative Modeling Flow-Based Generative Modeling

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Mar 12, 2026

Curriculum Sampling: A Two-Phase Curriculum for Efficient Training of Flow Matching

Timestep sampling

p(t)

is a central design choice in Flow Matching models, yet common practice increasingly favors static middle-biased distributions (e.g., Logit-Normal). We show that this choice induces a speed--quality trade-off: middle-biased sampling accelerates early convergence but yields worse asymptotic fidelity than Uniform sampling. By analyzing per-timestep training losses, we identify a U-shaped difficulty profile with persistent errors near the boundary regimes, implying that under-sampling the endpoints leaves fine details unresolved. Guided by this insight, we propose Curriculum Sampling, a two-phase schedule that begins with middle-biased sampling for rapid structure learning and then switches to Uniform sampling for boundary refinement. On CIFAR-10, Curriculum Sampling improves the best FID from

3.85

(Uniform) to

3.22

while reaching peak performance at

100

k rather than

150

k training steps. Our results highlight that timestep sampling should be treated as an evolving curriculum rather than a fixed hyperparameter.

Pengwei Sun

Stanford University

Flow Matching Flow-Based Generative Modeling Curriculum Learning

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Abstract

Few-Step Diffusion Sampling

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